Computer modeling of complex liquids and biological systems is an important tool in biochemistry. With the increasing power of modern computers it is becoming possible to design new drugS and new biomimetic materials, and to gain understanding of molecular recognition, and the effects of mutationS on protein folding. One of the major aims of this proposal is the invention, extension and application of new methods to accelerate the stimulation and sampling of conformational states of biomolecular systems. We aim to further develop methods invented during the last grant period to treat systems with multiple time scales such as our reversible reference system propagator algorithms. Monte Carlo and molecular dynamics methods for sampling conformational states of biomolecules are often inherently quasi-ergodic. This means that starting in one stable conformation, not all other conformations can be reached on a practical time scale. We aim to devise methods for sampling conformation space in protein systems and other systems characterized by rough energy landscapes, and to apply these new methods to important problems involving the binding of peptides to enzymes and to conformational transitions of peptides. We aim to develop next generation polarizable force fields in order to deal a major impediment to rational drug design. Predictions of binding energies are dependent on the quality of the force field. Existing force fields do not account for known changes in atomic charges when a peptide undergoes a conformation change. Such effects require a chemically accurate polarizable force field that can correctly account for specific hydrogen bonding energies. During the preceding grant period we introduced a simple force field based on the principle of electronegativity equalization which has had remarkable success in predicting properties of water, NMA and analine dipeptide. We have shown that this model correctly accounts for three-body energies of many different kinds of trimers (eg clusters of analine dipeptide and water molecules). One of the major objectives of this proposal is to devise next generation polarizable force fields for peptides capable of giving chemical accuracy in the calculation of binding free energies when properly implemented in simulations using the new sampling methods discussed above. The proposed research will provide new methods and algorithms as well as a next generation force field for use in biological simulations. These methods will be used to study the binding of cyclosporin A to cyclophilin and the conformational transitions in HIV-1 protease.